Spectrometers based on dispersive optical elements or optical interference phenomena are well-known instruments commonly applied for the measurement of the absolute wavelength and bandwidth of light sources. When employed as a bandwidth-measuring tool (“bandwidth meter”), the effect of the finite impulse response of the spectrometer must be considered when determining the actual bandwidth of the source being measured. For the purpose of the present application, “bandwidth” may refer to any number of metrics or mathematical constructions related to the details of the optical source spectrum, such as full-width of the spectrum at half-maximum peak intensity (FWHM), full-width at some percentage “X” of the peak intensity (FWXM), width of the 95%-enclosed energy integral about the peak (I95% or E95%), etc. An accurate knowledge of the bandwidth of an optical source is very important for many scientific and industrial applications, for example in spectroscopy of liquids and gases, critical dimension control in deep-ultraviolet (DUV) semiconductor photolithography, etc.
In very simple cases, for example when the spectrum of the source and the spectrometer impulse response are accurately represented both by purely Gaussian or both by purely Lorentzian functions, the effect of the spectrometer impulse response can easily be accounted for using simple algebraic equations for many bandwidth metrics. The output spectra of most optical sources, e.g., lasers, do not have such simple forms in general and may change with time or operating condition. Further, the impulse response of the spectrometer may be similarly complex or unknown.
A common method employed to surmount these obstacles is to employ a spectrometer whose impulse response has a bandwidth so narrow in comparison to the expected bandwidth of the source to be measured that its influence is negligible. That is, the spectrometer impulse response is well-approximated by a mathematical delta-function for the case in question. However, it is not always practical or even possible to obtain a spectrometer with such a narrow-bandwidth impulse response, particularly when it is required to be very narrow in comparison to a source such as a laser which itself may be extremely narrow (tens of femtometers or less on a wavelength scale).
A second and somewhat more sophisticated method commonly used approximates the spectrometer impulse response function and the source spectrum with analytic functions (e.g., of Lorentzian, Gaussian, or mixed type) for which the effects of convolution within the spectrometer can be calculated beforehand and then expressed in simple mathematical terms. As noted above, this is not necessarily a good approximation, and can fail or become very difficult to implement dependably for certain types of bandwidth metrics. Calculation of integral bandwidth metrics such as E95% can be inaccurate or very computationally intensive using this technique.
As an illustration of second method and its shortcomings, consider a recently released product of Cymer, Inc., the owner by assignment of the present application. This product, the XLA-100, contains an onboard bandwidth meter employing a single etalon with a FWHM bandpass of about 0.12 pico-meter (pm) that is used to interrogate the output of a deep-ultraviolet excimer laser light source having an average typical FWHM bandwidth of about 0.17 pm. The above approximation is made in which both the laser and the etalon spectrometer are assumed to have an analytic Lorentzian spectral shape; therefore, the FWHM of the etalon spectrometer fringe is found mathematically to be simply the sum of the FWHMs of the laser source and the etalon spectrometer impulse response. In this Lorentzian approximation, then, the actual laser source bandwidth is estimated by the FWHM of the etalon spectrometer fringe, minus the FWHM of the etalon spectrometer impulse response (determined in independent measurements). However, because the ratio of the FWHM bandwidths of the source spectrum and impulse response function is close to unity, this method may lose accuracy in the event that the shape of the laser spectrum deviates too far from an approximately-Lorentzian shape. For example, a narrowing of the central spectral peak of the source spectrum with a concomitant increase in energy in the near wings can result in an over-estimation of the FWHM bandwidth in this approximation.
If the detailed shape of the laser spectrum is constant, the offset subtracted in this example can sometimes be adjusted to compensate. However, if the shape of the laser spectrum changes with operating conditions, with system alignment, or over the lifetime of the product, even this compensation will not remain accurate. Also at issues is the complicating possibility that in a manufacturing setting, the etalon spectrometer may be tested and offset-calibrated on one laser, but is ultimately be installed on another that has a slightly different spectral shape. In this case the calibration may be in error.
It is the purpose of this invention to mitigate these and similar measurement errors by employing more than one spectrometer operating in parallel within a single bandwidth meter, where the multiple spectrometer sub-circuits have significantly different impulse response function bandwidths. Because each sub-circuit has a different bandpass, each sub-circuit has a correspondingly different relative sensitivity to energy content in various regions of the spectrum. For example, a fringe FWHM measurement of the output of a very narrow bandpass circuit will give a result that accurately approximates the FWHM of the source spectrum, but a fringe FWHM measurement of a very wide bandpass circuit will give a result that is more closely related to the total energy content of the source spectrum. By choosing the bandwidth of the impulse response functions of the sub-circuits carefully, it is possible to mitigate the errors described above and simultaneously provide accurate estimates of integral bandwidth metrics such as the E95 width using only simple algebraic equations. A significant advantage of the invention is that these simple equations can be handled with little computational overhead, important for real-time applications such as bandwidth monitoring or sensing in high-repetition-rate pulsed lasers.